Randomized Newton methods for large least-squares problems
Thursday, February 22, 2018
3:30PM – 5PM
We discuss randomized Newton and randomized quasi-Newton approaches to efficiently solve large linear least-squares problems, where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In our proposed framework, stochasticity is introduced as a means to overcome computational limitations, and probability distributions that can exploit structure and/or sparsity are considered. Our results show, in particular, that randomized Newton iterates, in contrast to randomized quasi-Newton iterates, may not converge to the desired least-squares solution. Numerical examples, including an example from extreme learning machines, demonstrate the potential applications of these methods.
Matthias (Tia) Chung is an Assistant Professor in the Department of Mathematics at Virginia Tech and member of the Computational Modeling and Data Analytics division in the Academy of Integrated Science. He joined the Virginia Tech in 2012, holds a Dipl. math. (Master of Science equivalent) from the University of Hamburg, Germany, and a Dr. rer. nat. (Ph.D. equivalent degree) in Computational Mathematics from the University of Lübeck, Germany. Before joining Virginia Tech, he was a Post-Doctoral Fellow at Emory University and Assistant Professor at Texas State University. Matthias Chung is an active member of the Society for Industrial and Applied Mathematics (SIAM) and its CSE, UQ, IS, and LA activity groups.
Matthias Chung’s research concerns various forms of cross-disciplinary inverse problems. Driven by its application, he and his lab develops and analyzes efficient numerical methods for inverse problems. Applications of interest include, but are not limited to, systems biology, medical and geophysical imaging, and dynamical systems. Challenges such as ill-posedness, large-scale, and uncertainty estimates are addressed by utilizing tools from and developing methods for regularization, randomized methods, stochastic learning, Bayesian inversion, and optimization. Research project are supported by NSF, NIH, and USDA.
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